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ApplyDetailedBalanceMD v1

Summary

Apply detailed balance to MDEventWorkspace

Properties

Name	Direction	Type	Default	Description
InputWorkspace	Input	MDEventWorkspace	Mandatory	An input MDEventWorkspace. Must be in Q_sample/Q_lab frame. Must have an axis as DeltaE
Temperature	Input	string		SampleLog variable name that contains the temperature or a number
OutputWorkspace	Output	MDEventWorkspace	Mandatory	The output MDEventWorkspace with detailed balance applied

Description

The fluctuation dissipation theorem [1,2] relates the dynamic susceptibility to the scattering function

\(\left(1-e^{-\frac{E}{k_B T}}\right) S(\mathbf{q}, E) = \frac{1}{\pi} \chi'' (\mathbf{q}, E)\)

For the MD events, the detailed balance is calculated and applied as below.

\(F = \pi(1-e^{-\frac{\Delta E}{k_B T(i)}})\)

\(I *= F\)

\(Err^2 *= F^2\)

where \(E\) is the energy transfer to the system. The algorithm assumes that the signal of the input workspace contains the scattering function \(S\). The signal of the output workspace will contain the dynamic susceptibility. The temperature is either extracted as the average of the values stored in the appropriate entry of the log attached to the workspace (user supplies the name of the entry) or user can pass a number for the temperature.

[1] S. W. Lovesey - Theory of Neutron Scattering from Condensed Matter, vol 1

[2] I. A. Zaliznyak and S. H. Lee - Magnetic Neutron Scattering in “Modern techniques for characterizing magnetic materials”

Usage

Example - Run Applied Detailed Balance

we1 = CreateSampleWorkspace(WorkspaceType='Event',
                           Function='Flat background',
                           BankPixelWidth=1,
                           XUnit='DeltaE',
                           XMin=-10,
                           XMax=19,
                           BinWidth=0.5)

AddSampleLog(Workspace=we1,LogName='Ei', LogText='20.', LogType='Number')
MoveInstrumentComponent(Workspace=we1, ComponentName='bank1', X=3, Z=3, RelativePosition=False)
MoveInstrumentComponent(Workspace=we1, ComponentName='bank2', X=-3, Z=-3, RelativePosition=False)
AddSampleLog(Workspace=we1,LogName='SampleTemp', LogText='25.0', LogType='Number Series')
SetGoniometer(Workspace=we1, Axis0='0,0,1,0,1')

# old way
weadb1 = ApplyDetailedBalance(InputWorkspace=we1, Temperature='SampleTemp')
mdabd1 = ConvertToMD(InputWorkspace=weadb1, QDimensions='Q3D')

# use algorithm ApplyDetailedBalanceMD
md1 = ConvertToMD(InputWorkspace=we1, QDimensions='Q3D')
test_db_md = ApplyDetailedBalanceMD(md1, 'SampleTemp')

r = CompareMDWorkspaces(test_db_md, mdabd1, CheckEvents=True, Tolerance=0.00001)
print('Number of MDEvents: {} == {}'.format(test_db_md.getNEvents(), mdabd1.getNEvents()))
print('Workspaces are {} equal'.format(r.Equals))

Output:

Number of MDEvents: 1972 == 1972
Workspaces are True equal

Categories: AlgorithmIndex | MDAlgorithms

Source

C++ header: ApplyDetailedBalanceMD.h

C++ source: ApplyDetailedBalanceMD.cpp